People born in the Middle East but residing in the Netherlands: Invariant population size estimates and the role of active and passive covariates

TL;DR

This paper explores how covariates affect population size estimates in register-based studies, distinguishing between active and passive covariates, and demonstrates the invariance of estimates under certain conditions, with an application to Middle Eastern residents in the Netherlands.

Contribution

It introduces the concept of passive and active covariates in loglinear models and characterizes when population size estimates remain invariant under marginalization.

Findings

Population size invariance is linked to collapsibility of contingency table margins.

Passive covariates can be included to refine population descriptions.

The method is illustrated with Middle Eastern residents in the Netherlands.

Abstract

Including covariates in loglinear models of population registers improves population size estimates for two reasons. First, it is possible to take heterogeneity of inclusion probabilities over the levels of a covariate into account; and second, it allows subdivision of the estimated population by the levels of the covariates, giving insight into characteristics of individuals that are not included in any of the registers. The issue of whether or not marginalizing the full table of registers by covariates over one or more covariates leaves the estimated population size estimate invariant is intimately related to collapsibility of contingency tables [Biometrika 70 (1983) 567-578]. We show that, with information from two registers, population size invariance is equivalent to the simultaneous collapsibility of each margin consisting of one register and the covariates. We give a short path characterization of the loglinear model which describes when marginalizing over a covariate leads to different population size estimates. Covariates that are collapsible are called passive, to distinguish them from covariates that are not collapsible and are termed active. We make the case that it can be useful to include passive covariates within the estimation model, because they allow a finer description of the population in terms of these covariates. As an example we discuss the estimation of the population size of people born in the Middle East but residing in the Netherlands.